David Letterman, seen during a taping of the "Late Show with David Letterman" on April 2, 2014, in New York, will announce his retirement on the show April 3. He will leave the show in 2015. (Photo by Greg Allen/Invision/AP)

On tonight’s “Late Show,” on CBS, television host David Letterman announced that he will retire in 2015.

During the taping of tonight’s show, Letterman told CBS president and CEO Leslie Moonves that he will step down as host of his late-night talk show when his current contract expires.

“The man who owns this network, Leslie Moonves, he and I have had a relationship for years and years and years, and we have had this conversation in the past,” Letterman told the audience, “and we agreed that we would work together on this circumstance and the timing of this circumstance. And I phoned him just before the program and I said, ‘Leslie, it’s been great, you’ve been great, and the network has been great, but I’m retiring.’

“I just want to reiterate my thanks for the support from the network, all of the people who have worked here, all of the people in the theater, all of the people on the staff, everybody at home, thank you very much,” Letterman continued.

“What this means now,” he quipped, “is that Paul (Shaffer, longtime Letterman bandleader) and I can be married.”

“We don’t have the timetable for this precisely down -- I think it will be at least a year or so, but sometime in the not too distant future, 2015 for the love of God, in fact, Paul and I will be wrapping things up,” he told the audience in the Ed Sullivan Theater.

CBS’ Moonves was even more complimentary about the often-prickly Letterman.

“When Dave decided on a one-year extension for his most recent contract, we knew this day was getting closer, but that doesn’t make the moment any less poignant for us,” the CBS executive said in a statement. “For 21 years, David Letterman has graced our network’s air in late night with wit, gravitas and brilliance unique in the history of our medium. During that time, Dave has given television audiences thousands of hours of comedic entertainment, the sharpest interviews in late night, and brilliant moments of candor and perspective around national events. He’s also managed to keep many celebrities, politicians and executives on their toes — including me.”

Moonves continued: “There is only one David Letterman. His greatness will always be remembered here, and he will certainly sit among the pantheon of this business. On a personal note, it’s been a privilege to get to know Dave and to enjoy a terrific relationship. It’s going to be tough to say goodbye. Fortunately, we won’t have to do that for another year or so. Until then, we look forward to celebrating Dave’s remarkable show and incredible talents.”

Letterman has hosted “The Late Show” on CBS since 1993, prior to which he hosted NBC’s “Late Night” from 1982 to 1992.

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Letterman turns 67 next week. He has the longest tenure of any late-night talk show host in U.S. television history, nearing 32 years since he created “Late Night” at NBC in 1982. He hosted that show through 1992, and in 1993 created CBS’ “The Late Show,” which he has hosted ever since.

Both shows have been nominated for a total of 108 Emmy Awards, winning eight. Letterman received Kennedy Center honors in 2012.

Leno retired from “The Tonight Show” earlier this year, making way for “Late Night” host Jimmy Fallon to take over the NBC institution.

But in an interview with Howard Stern in January, Letterman said that Leno’s departure would have no impact on how much longer he might stay as host of “Late Show.”

“I would do it forever if it were up to me,” said Letterman, before adding a wry aside: “Sometimes, it isn’t up to me.”

With the late-night landscape now settling at NBC, Who Replaces Letterman becomes the new guessing game. In the wings as a likely heir: Craig Ferguson, host of “The Late Late Show,” which follows Letterman.